"Congress reaffirmed that fact with its passage of the bipartisan Born-Alive Infants Protection Act in 2002. I support that law, which is still in effect. There is no need for additional federal legislation on this topic," Kaine said.

Monday's vote comes after Virginia Gov. Ralph Northam (D) provoked outrage among anti-abortion groups, GOP lawmakers and the White House over his comments about a bill that would have made it easier for women to get third-trimester abortions if their health was threatened by pregnancy.

Kathy Tran, the sponsor of the Virginia bill, fueled the political firestorm when her comments acknowledging that the legislation would allow a woman who is dilating to request an abortion if a doctor determined that childbirth would impair her mental or physical health went viral.

Northam further inflamed tensions when he said on a local radio show that third-trimester abortions are rare and typically occur when an infant is severely deformed or unable to survive after birth.

"In this particular example, if a mother is in labor, I can tell you exactly what would happen: the infant would be delivered; the infant would be kept comfortable; the infant would be resuscitated if that's what the mother and the family desired. And then a discussion would ensue between the physicians and the mother," Northam said.

A spokeswoman for Northam told The Washington Post that his comments were being taken out of context by Republicans.